1. Field of the Invention
The invention relates generally to linear filter circuits and, more particularly, but not by way of limitation, it relates to improvements in active RC filter circuitry, delay networks, and cascaded filter network.
2. Description of the Prior Art
It is well known that any linear function may be expressed as the ratio of two power series in terms of the Laplace operator s. If the function is rational, the numerator and denominator series are factorable into the products of terms with real roots, (s + .beta.). or into terms with complex or imaginary roots, (s.sup.2 .alpha. S+.beta.). It is then never necessary to use higher than the second order in the operator s as a sum, since higher order terms may be formed by multiplying, or cascading, second order terms. Because of this mathematical property, networks realizing second order functions are extremely useful as building blocks to obtain an arbitrary transfer response. A number of networks have been devised to obtain specific second order functions, many of which now in general use, were introduced in the article "Active RC Synthesis" by Sallen and Key as published in 1955 by the Professional Group of Circuit Theory, now the proceedings of the IEEE. The addition of a loading element to one of the circuits of that article resulted in the well-known filter of Kerwin and Huelsman, U.S. Pat. No. 3,609,567, as issued on Sept. 28, 1971, which teaches the realization of complex zeros on the j .omega. axis as well as the provision of independently positioned complex poles.
There is a very important but difficult function class with left-half plane poles mirrored symmetrically by right-half plane zeros, called an all pass delay, which affects the phase of a signal as a function of frequency without affecting the magnitude. Such a function is used to provide a time delay, a phase equalizer, and is used in the realization of a Hilbert function. In the prior art it has been common to use expensive inductors or a multitude of active elements in the generation of such functions. U.S. Pat. No. 3,736,517 in the name of J.T. Lim presents an inductorless active filter for the all pass time delay function. Although it requires several times the number of active components of the present invention, this patent must be considered prior art with respect to the present teachings. Yet another U.S. Pat. No. 3,919,658 in the name of J. J. Friend represents the best prior art known to Applicant which is directed to a realization of a second order all pass time delay function through utilization of a hybrid form of resistance and capacitance interconnection.
In contrast to the multiplicity of special purpose circuits which are present in the prior art, some such as the more well-known all pass delay circuits being quite complex, the present invention offers a simple standard form that is capable of being connected to realize any order of rational function, either by cascading second order sections of itself for optimum stability, or as used directly as one network with only a single active element to enable optimum economy.
Therefore, it is an object of the present invention to provide a universal, inductorless, single operational amplifier filter network form which is capable of directly realizing any arbitrary theoretically realizable linear transfer function.
It is a further object of the invention to provide a universal building block single operational amplifier active filter, which because of arbitrary second order pole-zero realization capability, essentially zero output impedance, and controlled gain, may be directly cascaded to realize any theoretically realizable linear transfer function.
Finally, it is an object of the present invention to provide an inductorless all pass delay network which requires only one operational amplifier for the realization of an arbitrary number of roots.
Other objects and advantages of the invention will be evident from the following detailed description when read in conjunction with the accompanying drawings which illustrate the invention.